Given the arithmetic sequence a_n = 4 - 3(n - 1), what is the domain for n?

Solution:

An arithmetic sequence is a list of numbers in which the difference between consecutive terms is constant.

Given a_n = 4 - 3(n - 1)

⇒ a_n = 4 - 3n + 3

⇒ a_n = 7 - 3n

a_n in an AP refers to the nth term of the sequence. The set of values given for n forms its domain.

Give values for n as N = {1, 2, 3, 4, .......}

a₁ = 7-3 = 4

a₂ = 7-6 = 1

a₃ = 7-9 = -2

a₄ = 7-12 = -5

a₅ = 7-15 = -8 and so on.

Thus domain for n is a natural number as n represents the the order of the term in the sequence..

Given the arithmetic sequence a_n = 4 - 3(n - 1), what is the domain for n?

Summary:

For the arithmetic sequence, a_n = 4 - 3(n - 1), domain for n is a natural number as n represents the order of the term in the sequence..